A damper includes a piston arranged in sliding engagement inside a pressure tube. The piston divides the pressure tube into a first working chamber and a second working chamber. A hydraulic compression stop assembly is positioned within the second working chamber and includes a plunger arranged in sliding engagement with a sleeve. The plunger includes a bumper cavity having a side wall. The bumper cavity extends a cavity depth from an end face of the plunger. The bumper cavity is in receipt of a compliant bumper. The bumper includes a bumper height greater than the cavity depth such that a portion of the bumper protrudes from the bumper cavity. The protruding bumper portion limits a maximum amount the bumper may be compressed before the sidewall is loaded by one of the piston and a piston rod.